I think the answer is purely,
accuracy.
Here is a quick summation of most of the actually documented fights between Hickok and those that he killed. Please note that it is difficult to say the .36 demonstrates "stopping power", and in fact when the .36 ball does "drop" a man, it would've probably been as effective a shot had Hickok been using a single action shooting .22LR 
1865
The Davis Tutt duel, 75 yards, and Tutt is hit in the chest below the 5th rib, the ball traveled across the chest cavity
likely damaging the heart.
Tutt called out, "Boys, I'm killed,"
ran onto the porch of the local courthouse and back to the street, where he collapsed and died,
1867
Hickok reportedly was involved in a dispute with drunken cowboys inside a saloon. One of them pushed him, causing him to drop his drink. Hickok struck the man, and four of the cowboy's friends rose with guns drawn. Hickok persuaded the men to step outside where he faced all four at 15 paces, or about 40 feet (12 m). The bartender counted down and Hickok
killed three of the men with a bullet to the head and wounded the fourth with a shot through the cheek bone
1869,
Bill Mulvey leveled his cocked rifle at Hickok. Hickok waved his hand past Mulvey at some onlookers and yelled, "Don't shoot him in the back; he is drunk." Mulvey wheeled his horse around to face those who might shoot him from behind, and before he realized he had been fooled,
Hickok shot him through the temple
Later in the same year Samuel Strawhun, a cowboy, who "made remarks against Hickok," and Hickok killed him with a
shot through the head.
1871
In an instant, Hickok pulled the triggers again sending two bullets into Coe's abdomen, and Coe
lived a day or two after the shootout, then died.
There is another fight where Hickok only killed one of the two men that he shot, but the location of the wounds (he shot the fellow who died, twice) is unknown.
So from the above documentation, it seems that we can actually say instead of guessing, the Navy .36's used by Hickok were accurate, AND that Hickok seemed to like to aim for the head, and those not shot in the head, did not immediately become incapacitated.
LD
